Related papers: Time-periodic behaviour in one- and two-dimensiona…
We analyze the dynamics of two atoms with a short-ranged pair interaction in a one-dimensional harmonic trap with time-dependent frequency. Our analysis is focused on two representative cases: (i) a sudden change of the trapping frequency…
The spatio-temporally periodic (STP) potential is interesting in Physics due to the intimate coupling between its time and spatial components. In this paper we begin with a brief discussion of the dynamical behaviors of a single particle in…
Exponential averages that appear in integral fluctuation theorems can be recast as a sum over moments of thermodynamic observables. We use two examples to show that such moment series can exhibit non-uniform convergence in certain singular…
Moderate deviation principles for empirical measure processes associated with weakly interacting Markov processes are established. Two families of models are considered: the first corresponds to a system of interacting diffusions whereas…
When an amorphous solid is deformed cyclically, it may reach a steady state in which the paths of constituent particles trace out closed loops that repeat in each driving cycle. A remarkable variant has been noticed in simulations where the…
The limiting stability of invariant probability measures of time homogeneous transition semigroups for autonomous stochastic systems has been extensively discussed in the literature. In this paper we initially initiate a program to study…
The existence and search for thermodynamic phase transitions is of unfading interest. In this paper, we present numerical evidence of dynamical phase transitions occurring in boundary driven systems with a constrained integrated current. It…
The mechanical force from light -- radiation pressure -- provides an intrinsic nonlinear interaction. Consequently, optomechanical systems near their steady state, such as the canonical optical spring, can display non-analytic behavior as a…
A translation invariant system of interacting quantum anharmonic oscillators indexed by the elements of a simple cubic lattice $\mathbb{Z}^d$ is considered. The anharmonic potential is of general type, which in particular means that it…
Time crystals in periodically driven systems have initially been studied assuming either the ability to quench the Hamiltonian between different many-body regimes, the presence of disorder or long-range interactions. Here we propose the…
In this paper we calculate and visualize the dynamics of an ensemble of electrons trapping in an electrostatic wave of slowly increasing amplitude, illustrating that, despite disordering of particles in angle during the trapping transition…
A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered…
This paper is a sequel to Chaika and Krishnan [arXiv:1612.00434]. We again consider translation invariant measures on families of nearest-neighbor semi-infinite walks on the integer lattice Z^d. We assume that once walks meet, they…
We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case.…
Motivated by a general principle governing regulation mechanisms in biological cells, we investigate a general interaction scheme between different populations of particles and specific particles, referred to as agents. Assuming that each…
These notes focus on the description of the phases of matter in two dimensions. Firstly, we present a brief discussion of the phase diagrams of bidimensional interacting passive systems, and their numerical and experimental measurements.…
A time crystal is a macroscopic quantum system in periodic motion in its ground state, stable only if isolated from energy exchange with the environment. For this reason, coupling separate time crystals is challenging, and time crystals in…
We consider systems of agents interacting through topological interactions. These have been shown to play an important part in animal andhuman behavior. Precisely, the system consists of a finite number of particles characterized by their…
We consider an interacting particle system which models the sterile insect technique. It is the superposition of a generalized contact process with exchanges of particles on a finite cylinder with open boundaries (see Kuoch et al., 2017).…
Recent studies on the phenomenology of ageing in certain many-particle systems which are at a critical point of their non-equilibrium steady-states, are reviewed. Examples include the contact process, the parity-conserving…